To be able to compare different investments, you need some number to measure and quantify. This number is the Annual Percentage Yield or APY.
First off, APY is different from Annual Percentage Rate aka APR. In the past I wrote APR when I meant APY. This has since been corrected. The number you care about is the APY, which is the equivalent interest rate for holding something for a year. APR is the interest rate per period times the number of periods per year. This does not take into account compounding. Why is APR even used at all? They use APR for listing loans to make the interest on them appear smaller. Those banks and car salespeople are sneaky, sneaky.
Let’s take a look at CDs and consider why you need something like an APY to compare them. I will make an assumption that the rates will never change. Let’s say you have a CD that will give you 1% of the principal at the end of 3-months and another that will give you 4% of the principal at the end of a year.
Well, 4% is more than 1%, so I’ll choose the 4% one.
Wait. It takes a year to get the money back from the 4%, but only 3 months to get the 1% back. There are four 3-month periods in a year, so you could get 1% back 4 times, which is 4%. Wouldn’t that make the two the same?
Wait. That 4% interest for the 3-month CD is the APR. You’re not actually getting that much. At the end of the 3 months, you get your money back and 1%, which you can reinvest into another 3-month CD and get 1% back on your principal and interest gained on the 1st CD. Your gains at the end of a year would actually be (1.01)^4 or 1.04060401. That 1 is your principal, so your gains are 4.06%. 4.06% is the APY on the 3 month CD that gives you 1% back at the end of 3 months.
|Period||3 months||1 year|
Only when you look at APY do you see a bigger number, which is really how much the investment is worth. APY is also important when you have two options that have the same duration. You can have two 1-year CDs, which compound monthly versus daily. Let’s examine this more carefully and actually calculate APY for a general case.
|Period||1 year||1 year|
|Compounding Periods per year||12||365|
APY = (1 + APR/(# of compounding periods) )^(# of compounding periods)
CD #2 is a better choice since it has more compounding with the same APR.
The APY gives you a number that you can compare investments even if they are different in duration. The only reason you would pick something with a lower APY is when you think interest rates are going to change.